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Transverse Momentum Dependent Parton Distributions at an EIC

Transverse Momentum Dependent Parton Distributions at an EIC. Feng Yuan Lawrence Berkeley National Laboratory. Thank Hasch, Burton, Prokudin, and many others, INT-Write-up for the EIC. Kinematics compared to previous machines. Courtesy from Sichtermann-Vogelsang for EIC-White paper.

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Transverse Momentum Dependent Parton Distributions at an EIC

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  1. Transverse Momentum Dependent Parton Distributions at an EIC Feng Yuan Lawrence Berkeley National Laboratory Thank Hasch, Burton, Prokudin, and many others, INT-Write-up for the EIC

  2. Kinematics compared to previous machines Courtesy from Sichtermann-Vogelsang for EIC-White paper

  3. Physics programs • Spin and parton imaging of nucleon • Quark/gluon helicity distributions • Spin puzzle • 3-D imaging of partons (OAM) • Transverse coordinate space (GPDs) • Transverse momentum space (TMDs) • Gluon saturation in large nucleus at small-x • Electroweak physics, new physics beyond SM • Cross-links among the above, and … INT-Write-up, Boer, et al., arXive:1108.1713

  4. Wigner Distribution W(x,r,kt) d2ktdz d3r F.T. GPD Transverse Momentum Dependent PDF f(x,kt) Generalized Parton Distr. H(x,ξ,t) dx d2kt PDF f(x) Form Factors F1(Q),F2(Q)

  5. Transverse momentum dependent parton distribution • Straightforward extension • Spin average, helicity, and transversity distributions • Transverse momentum-spin correlations • Nontrivial distributions, STXPT • In quark model, depends on S- and P-wave interference Mulders and Qiu’s talks

  6. Deformation when nucleon is transversely polarized -0.5 0.5 0.0 0.5 ky 0.0 -0.5 kx Quark Sivers function fit to the SIDIS Data, Anselmino, et al. 20009 Lattice Calculation of the IP density of Up quark, QCDSF/UKQCD Coll., 2006

  7. Where can we learn TMDs • Semi-inclusive hadron production in deep inelastic scattering (SIDIS) • Drell-Yan lepton pair, photon pair productions in pp scattering • Dijet correlation in DIS • Relevant e+e- annihilation processes • …

  8. Semi-inclusive DIS • Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target

  9. Spin-orbital correlation • Leading order TMDs All these TMDs can be probed through different azimuthal angle distributions

  10. ST kT Two major contributions • Sivers effect in the distribution • Collins effect in the fragmentation • Other contributions… ST (PXkT) P (zk+pT) (k,sT) ~pTXsT

  11. Universality of the Collins Fragmentation ep--> e Pi X e+e---> Pi Pi X pp--> jet(->Pi) X Metz 02, Collins-Metz 02, Yuan 07, Gamberg-Mukherjee-Mulders 08,10 Meissner-Metz 0812.3783 Yuan-Zhou, 0903.4680 Exps: BELLE, HERMES, STAR, COMPASS

  12. Collins asymmetries in SIDIS Summarized in the EIC Write-up

  13. Collins effects in e+e- BELLE Coll., 2008 Collins functions extracted from the Data, Anselmino, et al., 2009

  14. Sivers effect • It is the final state interaction providing the phase to a nonzero SSA • Non-universality in general • Only in special case, we have “Special Universality” Brodsky,Hwang,Schmidt 02 Collins, 02; Ji,Yuan,02; Belitsky,Ji,Yuan,02

  15. Sivers asymmetries in SIDIS Non-zero Sivers effects Observed in SIDIS Jlab Hall A 3He

  16. Great Potential at the EIC • High precision, detailed study • Wide range of Q2 coverage, QCD dynamics • Sea quark TMDs • Gluon TMDs • Large transverse momentum, connecting to collinear factorization

  17. Electron-Ion Collider Projections: Impressive coverage on Q2, x, z, and PT √S=140,50,15 GeV

  18. Quark Sivers function extracted from the data Leading order fit, simple Gaussian assumption for the Sivers function There are still theoretical uncertainties In the fit: scale dependence, high order corrections, … Inner band is the impact from the planed EIC kinematics Alexei Prokudin, et al.

  19. Sea quark:

  20. Large transverse momentum • Only possible with the EIC • QCD dynamics, evolution effects • Q2 dependence • Pt dependence • Twist-three mechanism Qiu’s talk

  21. EIC coverage 120fb-1

  22. A unified picture (leading pt/Q) Transverse momentum dependent Collinear/ longitudinal PT ΛQCD PT Q << << Ji-Qiu-Vogelsang-Yuan,2006 Yuan-Zhou, 2009

  23. Collins-Soper-Sterman Resummation • Separate the singular and regular parts • TMD factorization in b-space Kang-Xiao-Yuan, 2011

  24. Collinear divergence--splitting • Sivers function Similar to the weighted asymmetry, and the splitting Vogelsang-Yuan, 2009

  25. Hard factor at one-loop order • Same as the spin-average case

  26. Final resum form • Sudakov the same

  27. Coefficients at one-loop order • Together with A(2), this resum at Next-to-leading-logarithmic level • Phenomenological implementation is underway • Unpolarized, Nadolsky et al, 2001 • ALL, Koike-Nagashima-Vogelsang 2006

  28. Directly working on TMDs Aybat-Collins-Qiu-Rogers, 2011

  29. Q2-dependence • Aybat-Prokudin-Rogers, 2011 Needs a cross check!

  30. TMD gluon distributions • It is not easy, because gluon does not couple to photon directly • Can be studied in two-particle processes Di-photon In pp Dijet In DIS Vogelsang-Yuan, 2007 Dominguez-Xiao-Yuan, 2010 Boer-Brodsky-Mulders-Pisano, 2010 Qiu-Schlegel-Vogelsang, 2011

  31. Summary • Wonderful physics associated with TMDs: nucleon tomography; spin-orbital correlation; QCD dynamics; • We have learned something from HERMES, COMPASS, Jlab, BELLE • Electron-ion collider is the ultimate machine to study TMDs

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